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                Rainbow的信号                </h1>
                <p>时间限制：3s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：128MB</p>			</div>
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                                <h3>题目描述</h3><p><p><span style="font-size: medium">Freda发明了传呼机之后，rainbow进一步改进了传呼机发送信息所使用的信号。由于现在是数字、信息时代，rainbow发明的信号用N个自然数表示。为了避免两个人的对话被大坏蛋VariantF偷听T_T，rainbow把对话分成A、B、C三部分，分别用a、b、c三个密码加密。现在Freda接到了rainbow的信息，她的首要工作就是解密。Freda了解到，这三部分的密码计算方式如下：<br />
在1~N这N个数中，等概率地选取两个数l、r，如果l&gt;r，则交换l、r。把信号中的第l个数到第r个数取出来，构成一个数列P。<br />
A部分对话的密码是数列P的xor和的数学期望值。xor和就是数列P中各个数异或之后得到的数； xor和的期望就是对于所有可能选取的l、r，所得到的数列的xor和的平均数。<br />
B部分对话的密码是数列P的and和的期望，定义类似于xor和。<br />
C部分对话的密码是数列P的or和的期望，定义类似于xor和。</span></p>
<p></p></p><hr/><h3>输入格式</h3><p><p><span style="font-size: medium">第一行一个正整数N。<br />
第二行N个自然数，表示Freda接到的信号。</span></p></p><hr/><h3>输出格式</h3><p><p><span style="font-size: medium">一行三个实数，分别表示xor和、and和、or和的期望，四舍五入保留3位小数，相邻两个实数之间用一个空格隔开。</span></p></p><hr/><h3>样例输入</h3><pre>样例输入1
2
4 5

样例输入2
3
1 0 1</pre><hr/><h3>样例输出</h3><pre>样例输出1
2.750 4.250 4.750

样例输出2
0.667 0.222 0.889</pre><hr/><h3>提示</h3><p>没有写明提示</p><hr/><h3>题目来源</h3><p>Poetize9</p>
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